When we solve \(G^2\) -MVC or \(G^2\) -MDS problems in the \(\mathsf {CONGEST}\)  or \(\mathsf {CONGESTED~CLIQUE}\)  model we require that at the end of the algorithm each node needs to know whether it is part of the vertex cover or the dominating set. We point out that nodes cannot decide locally (see [1]}) whether a given given vertex cover (or DS) has a 'good' approximation factor as it might approximate an optimal solution badly in some part of the graph while it still provides a good approximation on the whole graph.
